Systems and methods for determining optical flow

ABSTRACT

Systems, methods, and non-transitory computer-readable media can obtain a first video frame and a second video frame. The first video frame can be processed using a convolutional neural network to output a first set of feature maps. The second video frame can be processed using the convolutional neural network to output a second set of feature maps. The first set of feature maps and the second set of feature maps can be processed using a spatial matching layer of the convolutional neural network to determine an optical flow for at least one pixel.

FIELD OF THE INVENTION

The present technology relates to the field of determining optical flow.More particularly, the present technology relates to techniques fordetermining a motion of objects in images.

BACKGROUND

Today, people often utilize computing devices (or systems) for a widevariety of purposes. Users can operate their computing devices to, forexample, interact with one another, create content, share information,and access information.

In some instances, computing devices can be used to determine theoptical flow of pixels or objects in frames (e.g., images and/or videoframes). Generally, optical flow describes the motion, or displacement,of objects in a visual scene that is captured in a frame. The motion ofobjects can be determined, for example, by tracking the movement ofindividual pixels between frames. The movement of pixels can be measuredbased on direction (e.g., movement along the x-axis and y-axis), andmagnitude (e.g., the amount the respective pixel was displaced betweenthe frames). Optical flow can be utilized for various purposes. In oneexample, an optical flow determined for frames of a video can beutilized to compress the video.

SUMMARY

Various embodiments of the present disclosure can include systems,methods, and non-transitory computer readable media configured to obtaina first video frame and a second video frame. The first video frame canbe processed using a convolutional neural network to output a first setof feature maps. The second video frame can be processed using theconvolutional neural network to output a second set of feature maps. Thefirst set of feature maps and the second set of feature maps can beprocessed using a spatial matching layer of the convolutional neuralnetwork to determine an optical flow for at least one pixel.

In an embodiment, the systems, methods, and non-transitory computerreadable media are configured to determine an optical flow for the pixelalong an axis by averaging i) a first displacement measurement of thepixel across a first feature map in the first set of feature maps and afirst feature map in the second set of feature maps and ii) a seconddisplacement measurement of the pixel across a second feature map in thefirst set of feature maps and a second feature map in the second set offeature maps.

In an embodiment, the systems, methods, and non-transitory computerreadable media are configured to determine a correspondence between atleast one pixel in the first feature map in the first set and at leastone pixel the first feature map in the second set, determine the firstdisplacement measurement of the corresponding pixel between the firstfeature map in the first set and the first feature map in the second setalong the axis, determine a correspondence between at least one pixel inthe second feature map in the first set and at least one pixel thesecond feature map in the second set, and determine the seconddisplacement measurement of the pixel between the second feature map inthe first set and the second feature map in the second set along theaxis.

In an embodiment, the systems, methods, and non-transitory computerreadable media are configured to determine an optical flow for the pixelalong an axis based at least in part on a histogram that includes i) afirst displacement measurement of the pixel across a first feature mapin the first set of feature maps and a first feature map in the secondset of feature maps and ii) a second displacement measurement of thepixel across a second feature map in the first set of feature maps and asecond feature map in the second set of feature maps.

In an embodiment, the systems, methods, and non-transitory computerreadable media are configured to generate the histogram using the firstdisplacement measurement and the second displacement measurement,wherein the optical flow for the pixel along the axis based at least inpart on a maximum peak value in the histogram.

In an embodiment, the optical flow for the pixel provides at least apredicted direction of the pixel along an x-axis and a predicteddirection of the pixel along a y-axis.

In an embodiment, the optical flow for the pixel provides at least apredicted magnitude of the pixel along an x-axis and a predictedmagnitude of the pixel along a y-axis.

In an embodiment, the systems, methods, and non-transitory computerreadable media are configured to train the convolutional neural networkusing one or more optical flow training data sets.

In an embodiment, the systems, methods, and non-transitory computerreadable media configured to process a first video frame in at least onetraining data set using the convolutional neural network to output afirst set of test feature maps, process a second video frame in the atleast one training data set using the convolutional neural network tooutput a second set of test feature maps, process the first set of testfeature maps and the second set of test feature maps using the spatialmatching layer of the convolutional neural network to determine anoptical flow for at least one pixel, determine at least one inaccuracyin the optical flow for the pixel based on a ground truth optical flowfor the pixel, and adjust one or more weight values of one or morefilters associated with the convolutional neural network to minimize theinaccuracy.

In an embodiment, the systems, methods, and non-transitory computerreadable media are configured to input a representation of the firstvideo frame to at least one convolutional layer to output a set ofsignals, the convolutional layer being trained to apply at least oneconvolutional operation to the representation of the first video frame,wherein the at least one convolutional operation is based on one or morefilters to convolve the representation of the first video frame, the oneor more filters being weighted to predict an optical flow for one ormore pixels.

It should be appreciated that many other features, applications,embodiments, and/or variations of the disclosed technology will beapparent from the accompanying drawings and from the following detaileddescription. Additional and/or alternative implementations of thestructures, systems, non-transitory computer readable media, and methodsdescribed herein can be employed without departing from the principlesof the disclosed technology.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example system including an example optical flowmodule configured to determine optical flows for video content using oneor more convolutional neural networks, according to an embodiment of thepresent disclosure.

FIG. 2 illustrates an example convolutional neural network moduleconfigured to analyze video content to determine optical flow, accordingto an embodiment of the present disclosure.

FIG. 3 illustrates an example diagram of determining optical flow usinga convolutional neural network, according to an embodiment of thepresent disclosure.

FIG. 4 illustrates an example process for determining optical flow usinga convolutional neural network, according to various embodiments of thepresent disclosure.

FIG. 5 illustrates an example process for training a convolutionalneural network to determine optical flow, according to variousembodiments of the present disclosure.

FIG. 6 illustrates a network diagram of an example system including anexample social networking system that can be utilized in variousscenarios, according to an embodiment of the present disclosure.

FIG. 7 illustrates an example of a computer system or computing devicethat can be utilized in various scenarios, according to an embodiment ofthe present disclosure.

The figures depict various embodiments of the disclosed technology forpurposes of illustration only, wherein the figures use like referencenumerals to identify like elements. One skilled in the art will readilyrecognize from the following discussion that alternative embodiments ofthe structures and methods illustrated in the figures can be employedwithout departing from the principles of the disclosed technologydescribed herein.

DETAILED DESCRIPTION Approaches for Determining Optical Flow

People use computing devices (or systems) for a wide variety ofpurposes. As mentioned, computing devices can be used to determine theoptical flow of pixels or objects in frames (e.g., images and/or videoframes). The term “object” can include any surfaces and/or edges thatmay be included a frame. Generally, optical flow describes the motion,or displacement, of objects in a visual scene that is captured in aframe. The motion of objects can be determined, for example, by trackingthe displacement of individual pixels between frames. The displacementof pixels can be measured based on direction (e.g., movement along thex-axis, y-axis, and/or z-axis), and magnitude (e.g., the amount therespective pixel was displaced between the frames). Existing approachesfor determining optical flow can provide accurate measurements, however,such approaches are typically computationally expensive. Alternatively,other existing approaches can be computationally inexpensive but willtypically provide less accurate measurements of optical flow.Accordingly, such conventional approaches may not be effective inaddressing these and other problems arising in computer technology.

An improved approach rooted in computer technology overcomes theforegoing and other disadvantages associated with conventionalapproaches specifically arising in the realm of computer technology. Invarious embodiments, frames can be provided as input to a convolutionalneural network (CNN) to obtain a corresponding optical flow of pixels inthe frames. The CNN can be trained using optical flow training data.Once trained, the CNN can output, for each inputted frame, acorresponding set of feature maps. In various embodiments, the set offeature maps corresponding to a first frame and the set of feature mapscorresponding to a second frame can be inputted to a spatial matchinglayer of the CNN. The spatial matching layer can perform a pairwiseanalysis of feature maps from the set of feature maps for the firstframe and the set of feature maps for the second frame. In doing thisanalysis, the spatial matching layer can determine correspondencesbetween pixels in the two sets of feature maps and can determinerespective displacements of the pixels along an x-axis and a y-axis, forexample. These displacements can be evaluated using one or moretechniques (e.g., histograms) to determine respective optical flows forthe pixels along the x-axis and the y-axis, for example.

Optical flow can be utilized in various ways. In one example, opticalflow can be utilized to recognize and categorize any actions that arecaptured in the frames being analyzed. For example, if the framescapture an individual jumping, then the optical flow would suggest avelocity along the y-axis. Similarly, if the frames capture anindividual running, then the optical flow would suggest a velocity alongthe x-axis. In another example, optical flow can be extended torecognize and categorize a sport being played, as captured in the framesbeing analyzed. In some instances, optical flow can be utilized forsurveillance purposes. For example, motion patterns, as captured in theframes being analyzed, can be evaluated using optical flow and anymotion patterns that have been classified as being abnormal can bedetermined. In another example, the optical flow of the frames beinganalyzed can be utilized to perform object recognition. For example, acertain motion pattern, as determined using optical flow, can beevaluated to determine that an object captured in the frames is aparticular individual or some other object (e.g., cat, bowling ball,football field, etc.).

FIG. 1 illustrates an example system 100 including an example opticalflow module 102 configured to analyze video content using one or moreconvolutional neural networks (CNN), according to an embodiment of thepresent disclosure. As shown in the example of FIG. 1, the exampleoptical flow module 102 can include a content module 104 and aconvolutional neural network module 106. In some instances, the examplesystem 100 can include at least one data store 108. The components(e.g., modules, elements, etc.) shown in this figure and all figuresherein are exemplary only, and other implementations may includeadditional, fewer, integrated, or different components. Some componentsmay not be shown so as not to obscure relevant details.

In some embodiments, the optical flow module 102 can be implemented, inpart or in whole, as software, hardware, or any combination thereof. Ingeneral, a module as discussed herein can be associated with software,hardware, or any combination thereof. In some implementations, one ormore functions, tasks, and/or operations of modules can be carried outor performed by software routines, software processes, hardware, and/orany combination thereof. In some cases, the optical flow module 102 canbe implemented, in part or in whole, as software running on one or morecomputing devices or systems, such as on a user or client computingdevice. In one example, the optical flow module 102 or at least aportion thereof can be implemented as or within an application (e.g.,app), a program, or an applet, etc., running on a user computing deviceor a client computing system, such as the user device 710 of FIG. 7. Inanother example, the optical flow module 102 or at least a portionthereof can be implemented using one or more computing devices orsystems that include one or more servers, such as network servers orcloud servers. In some instances, the optical flow module 102 can, inpart or in whole, be implemented within or configured to operate inconjunction with a social networking system (or service), such as thesocial networking system 730 of FIG. 7.

The optical flow module 102 can be configured to communicate and/oroperate with the at least one data store 108, as shown in the examplesystem 100. The at least one data store 108 can be configured to storeand maintain various types of data. In some implementations, the atleast one data store 108 can store information associated with thesocial networking system (e.g., the social networking system 730 of FIG.7). The information associated with the social networking system caninclude data about users, social connections, social interactions,locations, geo-fenced areas, maps, places, events, pages, groups, posts,communications, content, feeds, account settings, privacy settings, asocial graph, and various other types of data. In some implementations,the at least one data store 108 can store information associated withusers, such as user identifiers, user information, profile information,user specified settings, content produced or posted by users, andvarious other types of user data. In some embodiments, the at least onedata store 108 can store media content including video content, whichcan be obtained by the optical flow module 102. In some instances, theat least one data store 108 can also store training data for trainingone or more convolutional neural networks to determine optical flow. Inone example, the training data can include, for example, one or moreground truth optical flow data sets that can be used to train aconvolutional neural network for predicting the optical flow of a set offrames, such as respective directions and magnitudes for pixels, orvoxels, corresponding to the set of frames. This training data may bereal data with a known ground truth (e.g., SINTEL data set), artificialdata whose ground truth has been determined using an existing opticalflow technique, and/or hand labeled optical flow data sets. It should beappreciated that many variations are possible.

The content module 104 can be configured to obtain and/or receive videocontent to be analyzed. The video content may be a set of images orvideo frames, or video files, for example. In various embodiments, thevideo content may be provided (e.g., uploaded) by users of a socialnetworking system and/or a content provider. In some embodiments, suchvideo content may be stored in the data store 108 and the content module104 can be configured to obtain the video content from the data store108.

The convolutional neural network module 106 can be configured to analyzevideo content, such as video content provided by the content module 104.In various embodiments, the convolutional neural network module 106 canevaluate the video content using one or more convolutional neuralnetworks that have each been configured to determine optical flow ofpixels, or objects, between a set of frames (e.g., a frame t and a framet+1) in the video content. More details regarding the convolutionalneural network module 106 will be provided below with reference to FIG.2.

FIG. 2 illustrates an example convolutional neural network module 202configured to analyze video content, according to an embodiment of thepresent disclosure. In some embodiments, the convolutional neuralnetwork module 106 of FIG. 1 can be implemented as the exampleconvolutional neural network module 202. As shown in FIG. 2, the exampleconvolutional neural network module 202 can include a training module204, a frame input module 206, a convolution module 208, and a spatialmatching module 210. The convolutional neural network module 202 canevaluate a first frame and a second frame of a video using a CNN todetermine optical flow between the first and second frames. In variousembodiments, the CNN can include one or more convolutional layers andone or more pooling layers. A spatial matching layer that is configuredto determine optical flow between the first frame and the second framecan be included in the CNN or may operate independently from the CNN,depending on the implementation. For example, the CNN can be trained tooutput corresponding feature maps for the first frame and the secondframe. The spatial matching layer can perform various spatial matchingtechniques using the feature maps for the first frame and the featuremaps for the second frame and output an optical flow. For example, theoptical flow can indicate, for one or more pixels, a correspondingdirection (e.g., along the x-axis and y-axis) and magnitude between thefirst and second frames. In some embodiments, pixels in the frames canbe correlated to objects that are recognized in the frames. In suchembodiments, the optical flow can indicate a corresponding direction andmagnitude for the objects.

The training module 204 can train the CNN to output, or predict, opticalflow information for a set of frames. In various embodiments, the outputcan be an optical flow prediction for one or more pixels, or objects, inthe set of frames. The training module 204 can train the convolutionalneural network to determine optical flow using ground truth trainingdata that may be obtained, for example, from a data store (e.g., thedata store 108 of FIG. 1). In some embodiments, when training theconvolutional neural network to predict optical flow, the trainingmodule 204 can utilize training data that includes ground truth opticalflow outputs for various video content (e.g., a direction and magnitudefor each pixel).

For example, to train the various layers in the CNN, the training module204 can process, or forward propagate, a first training frame and asecond training frame through the CNN and the convolutional layers ofthe CNN can produce a set of corresponding feature maps for the firsttraining frame and the second training frame. These feature maps can beutilized by a spatial matching layer to output optical flow informationfor the first training frame and the second training frame. This opticalflow information can describe a respective direction and magnitude forone or more pixels or objects in the first and second training frames.This optical flow information can be compared against the ground truthof the first and second training frames to measure any inaccuracies inthe output produced by the CNN. In various embodiments, suchinaccuracies can be reduced by performing a backpropagation through theCNN. During backpropagation, the training module 204 can adjust one ormore weight values of one or more filters associated with the variouslayers in the CNN in order to minimize the inaccuracies. By performingbackpropagation over a number of training iterations, optimal, orotherwise suitable, weight values can be determined for the filters ofthe convolutional neural network. In various embodiments, the spatialmatching layer does not have any corresponding weights. In suchembodiments, during backpropagation, weight values of one or morefilters associated with the convolutional layers in the CNN areadjusted.

Once trained, the frame input module 206 of the convolutional neuralnetwork module 202 can receive a set of frames for which the opticalflow is to be determined. For example, the frame input module 206 canreceive a first frame and a second frame. The first and second framesmay, but need not, be from the same video content. Further, the firstand second frames may, but need not, be frames that are consecutive intime. In various embodiments, the convolution module 208 can beconfigured to independently process each of the first frame and thesecond frame. When processing the first frame and the second frame, theconvolution module 208 can be configured to apply at least oneconvolutional operation to the video content using one or moreconvolutional layers. A convolutional operation can utilize at least onefilter to convolve the representation of the first frame, which cancause the representation of the first frame to be reduced in signalsize. Each convolutional layer can apply a respective convolutionaloperation to its received input signals and can generate correspondingoutput signals that may be inputted into a subsequent layer duringforward propagation. In some embodiments, the signals outputted from theconvolutional layers are inputted to one or more subsequentconvolutional layers. In some embodiments, the convolution module 208can be configured to perform one or more pooling operations in additionto the convolutional operations. Once the various convolutionaloperations have been performed, the CNN can output a corresponding setof feature maps for each of the first frame and the second frame.

The spatial matching module 210 can be configured to analyze the sets offeature maps outputted by the convolution module 208 to determine anoptical flow for the first and second frames. Since the first frame andthe second frame were both processed using the same, or a duplicate,CNN, the respective sets of feature maps for the first and second framewill include various types of feature maps that follow the sameordering. This allows the spatial matching module 210 to comparecorresponding feature maps for the first frame and the second frame.When comparing a feature map corresponding to the first frame and afeature map corresponding to the second frame, the spatial matchingmodule 210 can determine a correspondence, or best match, for some orall pixels in the first and second frames. Various approaches can beutilized for determining such correspondences including, for example,sum of squared differences (SSD). Based on the correspondences, thespatial matching module 210 can determine a corresponding displacementmeasurement of how much a pixel moved along the x-axis between the firstand second frames (delta x) and/or a displacement measurement of howmuch the pixel moved along the y-axis between the first and secondframes (delta y). The spatial matching module 210 can determine suchmeasurements for the pixel across each of the different feature mapsoutputted for the first and second frame. Thus, for example, if the CNNoutputs 512 feature maps for the first frame and 512 feature maps forthe second frame, then the spatial matching module 210 can determine arespective displacement measurement for movement of the pixel along thex-axis and the y-axis using each pair of the 512 feature maps.

In some embodiments, the spatial matching module 210 can average, forthe pixel, each of the displacement measurements along the x-axis todetermine the optical flow for the pixel along the x-axis. In suchembodiments, the spatial matching module 210 can also average, for thepixel, each of the displacement measurements along the y-axis todetermine the optical flow for the pixel along the y-axis. In someembodiments, the spatial matching module 210 can determine the opticalflow along the x-axis and y-axis by generating one or more histograms.For example, the spatial matching module 210 can generate a firsthistogram of the different displacement measurements of a pixel alongthe x-axis and a second histogram of the different displacementmeasurements of the pixel along the y-axis. The first and secondhistograms can include all of the displacement measurements that weremade across each of the different feature maps outputted for the firstand second frame. In some embodiments, the spatial matching module 210can use the first histogram to determine the maximum displacementmeasurement along the x-axis and this maximum displacement measurementcan be selected as the optical flow for the pixel along the x-axis.Similarly, the spatial matching module 210 can use the second histogramto determine the maximum displacement measurement along the y-axis andthis maximum displacement measurement can be selected as the opticalflow for the pixel along the y-axis.

FIG. 3 illustrates an example diagram 300 of determining optical flowusing a convolutional neural network, according to an embodiment of thepresent disclosure. In the example of FIG. 3, a first frame 302 can beinputted to a trained convolutional neural network (CNN) 304. In thisexample, the CNN 304 may include a first convolutional layer having 64filters, followed by a first pooling layer, followed by a secondconvolutional layer having 128 filters, followed by a second poolinglayer, followed by a third convolutional layer having 512 filters. TheCNN architecture can vary depending on the implementation. In thisexample, the first frame 302 can have a resolution of 256 pixels by 256pixels (256×256) and can be processed through the CNN 304 to output acorresponding set of feature maps 306. In this example, the CNN 304 canoutput 512 feature maps for the first frame 302 and each feature map canhave a resolution of 32 pixels by 32 pixels (32×32). The size and numberof the feature maps can vary depending on the architecture of the CNN(e.g., the number of pooling layers and/or filters used in the CNN 304).

Similarly, a second frame 308 can be inputted to the CNN 304. In thisexample, the second frame 308 can have a resolution of 256 pixels by 256pixels can be processed through the CNN 304 to output a correspondingset of feature maps 310. The CNN 304 can output 512 feature maps for thesecond frame 308 and each feature map can have a resolution of 32 pixelsby 32 pixels. The spatial matching layer 312 can determine and outputthe optical flow between the first frame 302 and second frame 308, forexample, along the x-axis 314 and the y-axis 316. In this example, thespatial matching layer 312 can perform a pairwise analysis using eachfeature map in the set of feature maps 306 corresponding to the firstframe 302 and each feature map in the set of feature maps 310corresponding to the second frame 308, as described above.

FIG. 4 illustrates an example method for determining optical flow usinga convolutional neural network, according to an embodiment of thepresent disclosure. It should be appreciated that there can beadditional, fewer, or alternative steps performed in similar oralternative orders, or in parallel, within the scope of the variousembodiments discussed herein unless otherwise stated. At block 402, theexample method 400 can obtain a first video frame and a second videoframe. At block 404, the first video frame can be processed using aconvolutional neural network to output a first set of feature maps. Atblock 406, the second video frame can be processed using theconvolutional neural network to output a second set of feature maps. Atblock 408, the first set of feature maps and the second set of featuremaps can be processed using a spatial matching layer of theconvolutional neural network to determine an optical flow for at leastone pixel.

FIG. 5 illustrates an example method for training a convolutional neuralnetwork to determine optical flow, according to an embodiment of thepresent disclosure. It should be appreciated that there can beadditional, fewer, or alternative steps performed in similar oralternative orders, or in parallel, within the scope of the variousembodiments discussed herein unless otherwise stated. At block 502, theexample method 500 can process a first video frame in a training dataset using a convolutional neural network to output a first set of testfeature maps. At block 504, the example method 500 can process a secondvideo frame in a training data set using a convolutional neural networkto output a second set of test feature maps. At block 506, the examplemethod 500 can process the first set of test feature maps and the secondset of test feature maps using a spatial matching layer of theconvolutional neural network to determine an optical flow for at leastone pixel. At block 508, the example method 500 can determine at leastone inaccuracy in the optical flow for the pixel based on a ground truthoptical flow for the pixel. At block 510, the example method 500 canadjust one or more weight values of one or more filters associated withthe convolutional neural network to minimize the inaccuracy.

It is contemplated that there can be many other uses, applications,and/or variations associated with the various embodiments of the presentdisclosure. For example, in some cases, user can choose whether or notto opt-in to utilize the disclosed technology. The disclosed technologycan also ensure that various privacy settings and preferences aremaintained and can prevent private information from being divulged. Inanother example, various embodiments of the present disclosure canlearn, improve, and/or be refined over time.

Social Networking System—Example Implementation

FIG. 6 illustrates a network diagram of an example system 600 that canbe utilized in various scenarios, in accordance with an embodiment ofthe present disclosure. The system 600 includes one or more user devices610, one or more external systems 620, a social networking system (orservice) 630, and a network 650. In an embodiment, the social networkingservice, provider, and/or system discussed in connection with theembodiments described above may be implemented as the social networkingsystem 630. For purposes of illustration, the embodiment of the system600, shown by FIG. 6, includes a single external system 620 and a singleuser device 610. However, in other embodiments, the system 600 mayinclude more user devices 610 and/or more external systems 620. Incertain embodiments, the social networking system 630 is operated by asocial network provider, whereas the external systems 620 are separatefrom the social networking system 630 in that they may be operated bydifferent entities. In various embodiments, however, the socialnetworking system 630 and the external systems 620 operate inconjunction to provide social networking services to users (or members)of the social networking system 630. In this sense, the socialnetworking system 630 provides a platform or backbone, which othersystems, such as external systems 620, may use to provide socialnetworking services and functionalities to users across the Internet.

The user device 610 comprises one or more computing devices (or systems)that can receive input from a user and transmit and receive data via thenetwork 650. In one embodiment, the user device 610 is a conventionalcomputer system executing, for example, a Microsoft Windows compatibleoperating system (OS), Apple OS X, and/or a Linux distribution. Inanother embodiment, the user device 610 can be a computing device or adevice having computer functionality, such as a smart-phone, a tablet, apersonal digital assistant (PDA), a mobile telephone, a laptop computer,a wearable device (e.g., a pair of glasses, a watch, a bracelet, etc.),a camera, an appliance, etc. The user device 610 is configured tocommunicate via the network 650. The user device 610 can execute anapplication, for example, a browser application that allows a user ofthe user device 610 to interact with the social networking system 630.In another embodiment, the user device 610 interacts with the socialnetworking system 630 through an application programming interface (API)provided by the native operating system of the user device 610, such asiOS and ANDROID. The user device 610 is configured to communicate withthe external system 620 and the social networking system 630 via thenetwork 650, which may comprise any combination of local area and/orwide area networks, using wired and/or wireless communication systems.

In one embodiment, the network 650 uses standard communicationstechnologies and protocols. Thus, the network 650 can include linksusing technologies such as Ethernet, 802.11, worldwide interoperabilityfor microwave access (WiMAX), 3G, 4G, CDMA, GSM, LTE, digital subscriberline (DSL), etc. Similarly, the networking protocols used on the network650 can include multiprotocol label switching (MPLS), transmissioncontrol protocol/Internet protocol (TCP/IP), User Datagram Protocol(UDP), hypertext transport protocol (HTTP), simple mail transferprotocol (SMTP), file transfer protocol (FTP), and the like. The dataexchanged over the network 650 can be represented using technologiesand/or formats including hypertext markup language (HTML) and extensiblemarkup language (XML). In addition, all or some links can be encryptedusing conventional encryption technologies such as secure sockets layer(SSL), transport layer security (TLS), and Internet Protocol security(IPsec).

In one embodiment, the user device 610 may display content from theexternal system 620 and/or from the social networking system 630 byprocessing a markup language document 614 received from the externalsystem 620 and from the social networking system 630 using a browserapplication 612. The markup language document 614 identifies content andone or more instructions describing formatting or presentation of thecontent. By executing the instructions included in the markup languagedocument 614, the browser application 612 displays the identifiedcontent using the format or presentation described by the markuplanguage document 614. For example, the markup language document 614includes instructions for generating and displaying a web page havingmultiple frames that include text and/or image data retrieved from theexternal system 620 and the social networking system 630. In variousembodiments, the markup language document 614 comprises a data fileincluding extensible markup language (XML) data, extensible hypertextmarkup language (XHTML) data, or other markup language data.Additionally, the markup language document 614 may include JavaScriptObject Notation (JSON) data, JSON with padding (JSONP), and JavaScriptdata to facilitate data-interchange between the external system 620 andthe user device 610. The browser application 612 on the user device 610may use a JavaScript compiler to decode the markup language document614.

The markup language document 614 may also include, or link to,applications or application frameworks such as FLASH™ or Unity™applications, the Silverlight™ application framework, etc.

In one embodiment, the user device 610 also includes one or more cookies616 including data indicating whether a user of the user device 610 islogged into the social networking system 630, which may enablemodification of the data communicated from the social networking system630 to the user device 610.

The external system 620 includes one or more web servers that includeone or more web pages 622 a, 622 b, which are communicated to the userdevice 610 using the network 650. The external system 620 is separatefrom the social networking system 630. For example, the external system620 is associated with a first domain, while the social networkingsystem 630 is associated with a separate social networking domain. Webpages 622 a, 622 b, included in the external system 620, comprise markuplanguage documents 614 identifying content and including instructionsspecifying formatting or presentation of the identified content. Asdiscussed previously, it should be appreciated that there can be manyvariations or other possibilities.

The social networking system 630 includes one or more computing devicesfor a social network, including a plurality of users, and providingusers of the social network with the ability to communicate and interactwith other users of the social network. In some instances, the socialnetwork can be represented by a graph, i.e., a data structure includingedges and nodes. Other data structures can also be used to represent thesocial network, including but not limited to databases, objects,classes, meta elements, files, or any other data structure. The socialnetworking system 630 may be administered, managed, or controlled by anoperator. The operator of the social networking system 630 may be ahuman being, an automated application, or a series of applications formanaging content, regulating policies, and collecting usage metricswithin the social networking system 630. Any type of operator may beused.

Users may join the social networking system 630 and then add connectionsto any number of other users of the social networking system 630 to whomthey desire to be connected. As used herein, the term “friend” refers toany other user of the social networking system 630 to whom a user hasformed a connection, association, or relationship via the socialnetworking system 630. For example, in an embodiment, if users in thesocial networking system 630 are represented as nodes in the socialgraph, the term “friend” can refer to an edge formed between anddirectly connecting two user nodes.

Connections may be added explicitly by a user or may be automaticallycreated by the social networking system 630 based on commoncharacteristics of the users (e.g., users who are alumni of the sameeducational institution). For example, a first user specifically selectsa particular other user to be a friend. Connections in the socialnetworking system 630 are usually in both directions, but need not be,so the terms “user” and “friend” depend on the frame of reference.Connections between users of the social networking system 630 areusually bilateral (“two-way”), or “mutual,” but connections may also beunilateral, or “one-way.” For example, if Bob and Joe are both users ofthe social networking system 630 and connected to each other, Bob andJoe are each other's connections. If, on the other hand, Bob wishes toconnect to Joe to view data communicated to the social networking system630 by Joe, but Joe does not wish to form a mutual connection, aunilateral connection may be established. The connection between usersmay be a direct connection; however, some embodiments of the socialnetworking system 630 allow the connection to be indirect via one ormore levels of connections or degrees of separation.

In addition to establishing and maintaining connections between usersand allowing interactions between users, the social networking system630 provides users with the ability to take actions on various types ofitems supported by the social networking system 630. These items mayinclude groups or networks (i.e., social networks of people, entities,and concepts) to which users of the social networking system 630 maybelong, events or calendar entries in which a user might be interested,computer-based applications that a user may use via the socialnetworking system 630, transactions that allow users to buy or sellitems via services provided by or through the social networking system630, and interactions with advertisements that a user may perform on oroff the social networking system 630. These are just a few examples ofthe items upon which a user may act on the social networking system 630,and many others are possible. A user may interact with anything that iscapable of being represented in the social networking system 630 or inthe external system 620, separate from the social networking system 630,or coupled to the social networking system 630 via the network 650.

The social networking system 630 is also capable of linking a variety ofentities. For example, the social networking system 630 enables users tointeract with each other as well as external systems 620 or otherentities through an API, a web service, or other communication channels.The social networking system 630 generates and maintains the “socialgraph” comprising a plurality of nodes interconnected by a plurality ofedges. Each node in the social graph may represent an entity that canact on another node and/or that can be acted on by another node. Thesocial graph may include various types of nodes. Examples of types ofnodes include users, non-person entities, content items, web pages,groups, activities, messages, concepts, and any other things that can berepresented by an object in the social networking system 630. An edgebetween two nodes in the social graph may represent a particular kind ofconnection, or association, between the two nodes, which may result fromnode relationships or from an action that was performed by one of thenodes on the other node. In some cases, the edges between nodes can beweighted. The weight of an edge can represent an attribute associatedwith the edge, such as a strength of the connection or associationbetween nodes. Different types of edges can be provided with differentweights. For example, an edge created when one user “likes” another usermay be given one weight, while an edge created when a user befriendsanother user may be given a different weight.

As an example, when a first user identifies a second user as a friend,an edge in the social graph is generated connecting a node representingthe first user and a second node representing the second user. Asvarious nodes relate or interact with each other, the social networkingsystem 630 modifies edges connecting the various nodes to reflect therelationships and interactions.

The social networking system 630 also includes user-generated content,which enhances a user's interactions with the social networking system630. User-generated content may include anything a user can add, upload,send, or “post” to the social networking system 630. For example, a usercommunicates posts to the social networking system 630 from a userdevice 610. Posts may include data such as status updates or othertextual data, location information, images such as photos, videos,links, music or other similar data and/or media. Content may also beadded to the social networking system 630 by a third party. Content“items” are represented as objects in the social networking system 630.In this way, users of the social networking system 630 are encouraged tocommunicate with each other by posting text and content items of varioustypes of media through various communication channels. Suchcommunication increases the interaction of users with each other andincreases the frequency with which users interact with the socialnetworking system 630.

The social networking system 630 includes a web server 632, an APIrequest server 634, a user profile store 636, a connection store 638, anaction logger 640, an activity log 642, and an authorization server 644.In an embodiment of the invention, the social networking system 630 mayinclude additional, fewer, or different components for variousapplications. Other components, such as network interfaces, securitymechanisms, load balancers, failover servers, management and networkoperations consoles, and the like are not shown so as to not obscure thedetails of the system.

The user profile store 636 maintains information about user accounts,including biographic, demographic, and other types of descriptiveinformation, such as work experience, educational history, hobbies orpreferences, location, and the like that has been declared by users orinferred by the social networking system 630. This information is storedin the user profile store 636 such that each user is uniquelyidentified. The social networking system 630 also stores data describingone or more connections between different users in the connection store638. The connection information may indicate users who have similar orcommon work experience, group memberships, hobbies, or educationalhistory. Additionally, the social networking system 630 includesuser-defined connections between different users, allowing users tospecify their relationships with other users. For example, user-definedconnections allow users to generate relationships with other users thatparallel the users' real-life relationships, such as friends,co-workers, partners, and so forth. Users may select from predefinedtypes of connections, or define their own connection types as needed.Connections with other nodes in the social networking system 630, suchas non-person entities, buckets, cluster centers, images, interests,pages, external systems, concepts, and the like are also stored in theconnection store 638.

The social networking system 630 maintains data about objects with whicha user may interact. To maintain this data, the user profile store 636and the connection store 638 store instances of the corresponding typeof objects maintained by the social networking system 630. Each objecttype has information fields that are suitable for storing informationappropriate to the type of object. For example, the user profile store636 contains data structures with fields suitable for describing auser's account and information related to a user's account. When a newobject of a particular type is created, the social networking system 630initializes a new data structure of the corresponding type, assigns aunique object identifier to it, and begins to add data to the object asneeded. This might occur, for example, when a user becomes a user of thesocial networking system 630, the social networking system 630 generatesa new instance of a user profile in the user profile store 636, assignsa unique identifier to the user account, and begins to populate thefields of the user account with information provided by the user.

The connection store 638 includes data structures suitable fordescribing a user's connections to other users, connections to externalsystems 620 or connections to other entities. The connection store 638may also associate a connection type with a user's connections, whichmay be used in conjunction with the user's privacy setting to regulateaccess to information about the user. In an embodiment of the invention,the user profile store 636 and the connection store 638 may beimplemented as a federated database.

Data stored in the connection store 638, the user profile store 636, andthe activity log 642 enables the social networking system 630 togenerate the social graph that uses nodes to identify various objectsand edges connecting nodes to identify relationships between differentobjects. For example, if a first user establishes a connection with asecond user in the social networking system 630, user accounts of thefirst user and the second user from the user profile store 636 may actas nodes in the social graph. The connection between the first user andthe second user stored by the connection store 638 is an edge betweenthe nodes associated with the first user and the second user. Continuingthis example, the second user may then send the first user a messagewithin the social networking system 630. The action of sending themessage, which may be stored, is another edge between the two nodes inthe social graph representing the first user and the second user.Additionally, the message itself may be identified and included in thesocial graph as another node connected to the nodes representing thefirst user and the second user.

In another example, a first user may tag a second user in an image thatis maintained by the social networking system 630 (or, alternatively, inan image maintained by another system outside of the social networkingsystem 630). The image may itself be represented as a node in the socialnetworking system 630. This tagging action may create edges between thefirst user and the second user as well as create an edge between each ofthe users and the image, which is also a node in the social graph. Inyet another example, if a user confirms attending an event, the user andthe event are nodes obtained from the user profile store 636, where theattendance of the event is an edge between the nodes that may beretrieved from the activity log 642. By generating and maintaining thesocial graph, the social networking system 630 includes data describingmany different types of objects and the interactions and connectionsamong those objects, providing a rich source of socially relevantinformation.

The web server 632 links the social networking system 630 to one or moreuser devices 610 and/or one or more external systems 620 via the network650. The web server 632 serves web pages, as well as other web-relatedcontent, such as Java, JavaScript, Flash, XML, and so forth. The webserver 632 may include a mail server or other messaging functionalityfor receiving and routing messages between the social networking system630 and one or more user devices 610. The messages can be instantmessages, queued messages (e.g., email), text and SMS messages, or anyother suitable messaging format.

The API request server 634 allows one or more external systems 620 anduser devices 610 to call access information from the social networkingsystem 630 by calling one or more API functions. The API request server634 may also allow external systems 620 to send information to thesocial networking system 630 by calling APIs. The external system 620,in one embodiment, sends an API request to the social networking system630 via the network 650, and the API request server 634 receives the APIrequest. The API request server 634 processes the request by calling anAPI associated with the API request to generate an appropriate response,which the API request server 634 communicates to the external system 620via the network 650. For example, responsive to an API request, the APIrequest server 634 collects data associated with a user, such as theuser's connections that have logged into the external system 620, andcommunicates the collected data to the external system 620. In anotherembodiment, the user device 610 communicates with the social networkingsystem 630 via APIs in the same manner as external systems 620.

The action logger 640 is capable of receiving communications from theweb server 632 about user actions on and/or off the social networkingsystem 630. The action logger 640 populates the activity log 642 withinformation about user actions, enabling the social networking system630 to discover various actions taken by its users within the socialnetworking system 630 and outside of the social networking system 630.Any action that a particular user takes with respect to another node onthe social networking system 630 may be associated with each user'saccount, through information maintained in the activity log 642 or in asimilar database or other data repository. Examples of actions taken bya user within the social networking system 630 that are identified andstored may include, for example, adding a connection to another user,sending a message to another user, reading a message from another user,viewing content associated with another user, attending an event postedby another user, posting an image, attempting to post an image, or otheractions interacting with another user or another object. When a usertakes an action within the social networking system 630, the action isrecorded in the activity log 642. In one embodiment, the socialnetworking system 630 maintains the activity log 642 as a database ofentries. When an action is taken within the social networking system630, an entry for the action is added to the activity log 642. Theactivity log 642 may be referred to as an action log.

Additionally, user actions may be associated with concepts and actionsthat occur within an entity outside of the social networking system 630,such as an external system 620 that is separate from the socialnetworking system 630. For example, the action logger 640 may receivedata describing a user's interaction with an external system 620 fromthe web server 632. In this example, the external system 620 reports auser's interaction according to structured actions and objects in thesocial graph.

Other examples of actions where a user interacts with an external system620 include a user expressing an interest in an external system 620 oranother entity, a user posting a comment to the social networking system630 that discusses an external system 620 or a web page 622 a within theexternal system 620, a user posting to the social networking system 630a Uniform Resource Locator (URL) or other identifier associated with anexternal system 620, a user attending an event associated with anexternal system 620, or any other action by a user that is related to anexternal system 620. Thus, the activity log 642 may include actionsdescribing interactions between a user of the social networking system630 and an external system 620 that is separate from the socialnetworking system 630.

The authorization server 644 enforces one or more privacy settings ofthe users of the social networking system 630. A privacy setting of auser determines how particular information associated with a user can beshared. The privacy setting comprises the specification of particularinformation associated with a user and the specification of the entityor entities with whom the information can be shared. Examples ofentities with which information can be shared may include other users,applications, external systems 620, or any entity that can potentiallyaccess the information. The information that can be shared by a usercomprises user account information, such as profile photos, phonenumbers associated with the user, user's connections, actions taken bythe user such as adding a connection, changing user profile information,and the like.

The privacy setting specification may be provided at different levels ofgranularity. For example, the privacy setting may identify specificinformation to be shared with other users; the privacy settingidentifies a work phone number or a specific set of related information,such as, personal information including profile photo, home phonenumber, and status. Alternatively, the privacy setting may apply to allthe information associated with the user. The specification of the setof entities that can access particular information can also be specifiedat various levels of granularity. Various sets of entities with whichinformation can be shared may include, for example, all friends of theuser, all friends of friends, all applications, or all external systems620. One embodiment allows the specification of the set of entities tocomprise an enumeration of entities. For example, the user may provide alist of external systems 620 that are allowed to access certaininformation. Another embodiment allows the specification to comprise aset of entities along with exceptions that are not allowed to access theinformation. For example, a user may allow all external systems 620 toaccess the user's work information, but specify a list of externalsystems 620 that are not allowed to access the work information. Certainembodiments call the list of exceptions that are not allowed to accesscertain information a “block list”. External systems 620 belonging to ablock list specified by a user are blocked from accessing theinformation specified in the privacy setting. Various combinations ofgranularity of specification of information, and granularity ofspecification of entities, with which information is shared arepossible. For example, all personal information may be shared withfriends whereas all work information may be shared with friends offriends.

The authorization server 644 contains logic to determine if certaininformation associated with a user can be accessed by a user's friends,external systems 620, and/or other applications and entities. Theexternal system 620 may need authorization from the authorization server644 to access the user's more private and sensitive information, such asthe user's work phone number. Based on the user's privacy settings, theauthorization server 644 determines if another user, the external system620, an application, or another entity is allowed to access informationassociated with the user, including information about actions taken bythe user.

In some embodiments, the social networking system 630 can include anoptical flow module 646. The optical flow module 646 can, for example,be implemented as the optical flow module 102 of FIG. 1. As discussedpreviously, it should be appreciated that there can be many variationsor other possibilities.

Hardware Implementation

The foregoing processes and features can be implemented by a widevariety of machine and computer system architectures and in a widevariety of network and computing environments. FIG. 7 illustrates anexample of a computer system 700 that may be used to implement one ormore of the embodiments described herein in accordance with anembodiment of the invention. The computer system 700 includes sets ofinstructions for causing the computer system 700 to perform theprocesses and features discussed herein. The computer system 700 may beconnected (e.g., networked) to other machines. In a networkeddeployment, the computer system 700 may operate in the capacity of aserver machine or a client machine in a client-server networkenvironment, or as a peer machine in a peer-to-peer (or distributed)network environment. In an embodiment of the invention, the computersystem 700 may be the social networking system 630, the user device 610,and the external system 720, or a component thereof. In an embodiment ofthe invention, the computer system 700 may be one server among many thatconstitutes all or part of the social networking system 630.

The computer system 700 includes a processor 702, a cache 704, and oneor more executable modules and drivers, stored on a computer-readablemedium, directed to the processes and features described herein.Additionally, the computer system 700 includes a high performanceinput/output (I/O) bus 706 and a standard I/O bus 708. A host bridge 710couples processor 702 to high performance I/O bus 706, whereas I/O busbridge 712 couples the two buses 706 and 708 to each other. A systemmemory 714 and one or more network interfaces 716 couple to highperformance I/O bus 706. The computer system 700 may further includevideo memory and a display device coupled to the video memory (notshown). Mass storage 718 and I/O ports 720 couple to the standard I/Obus 708. The computer system 700 may optionally include a keyboard andpointing device, a display device, or other input/output devices (notshown) coupled to the standard I/O bus 708. Collectively, these elementsare intended to represent a broad category of computer hardware systems,including but not limited to computer systems based on thex86-compatible processors manufactured by Intel Corporation of SantaClara, Calif., and the x86-compatible processors manufactured byAdvanced Micro Devices (AMD), Inc., of Sunnyvale, Calif., as well as anyother suitable processor.

An operating system manages and controls the operation of the computersystem 700, including the input and output of data to and from softwareapplications (not shown). The operating system provides an interfacebetween the software applications being executed on the system and thehardware components of the system. Any suitable operating system may beused, such as the LINUX Operating System, the Apple Macintosh OperatingSystem, available from Apple Computer Inc. of Cupertino, Calif., UNIXoperating systems, Microsoft® Windows® operating systems, BSD operatingsystems, and the like. Other implementations are possible.

The elements of the computer system 700 are described in greater detailbelow. In particular, the network interface 716 provides communicationbetween the computer system 700 and any of a wide range of networks,such as an Ethernet (e.g., IEEE 802.3) network, a backplane, etc. Themass storage 718 provides permanent storage for the data and programminginstructions to perform the above-described processes and featuresimplemented by the respective computing systems identified above,whereas the system memory 714 (e.g., DRAM) provides temporary storagefor the data and programming instructions when executed by the processor702. The I/O ports 720 may be one or more serial and/or parallelcommunication ports that provide communication between additionalperipheral devices, which may be coupled to the computer system 700.

The computer system 700 may include a variety of system architectures,and various components of the computer system 700 may be rearranged. Forexample, the cache 704 may be on-chip with processor 702. Alternatively,the cache 704 and the processor 702 may be packed together as a“processor module”, with processor 702 being referred to as the“processor core”. Furthermore, certain embodiments of the invention mayneither require nor include all of the above components. For example,peripheral devices coupled to the standard I/O bus 708 may couple to thehigh performance I/O bus 706. In addition, in some embodiments, only asingle bus may exist, with the components of the computer system 700being coupled to the single bus. Moreover, the computer system 700 mayinclude additional components, such as additional processors, storagedevices, or memories.

In general, the processes and features described herein may beimplemented as part of an operating system or a specific application,component, program, object, module, or series of instructions referredto as “programs”. For example, one or more programs may be used toexecute specific processes described herein. The programs typicallycomprise one or more instructions in various memory and storage devicesin the computer system 700 that, when read and executed by one or moreprocessors, cause the computer system 700 to perform operations toexecute the processes and features described herein. The processes andfeatures described herein may be implemented in software, firmware,hardware (e.g., an application specific integrated circuit), or anycombination thereof.

In one implementation, the processes and features described herein areimplemented as a series of executable modules run by the computer system700, individually or collectively in a distributed computingenvironment. The foregoing modules may be realized by hardware,executable modules stored on a computer-readable medium (ormachine-readable medium), or a combination of both. For example, themodules may comprise a plurality or series of instructions to beexecuted by a processor in a hardware system, such as the processor 702.Initially, the series of instructions may be stored on a storage device,such as the mass storage 718. However, the series of instructions can bestored on any suitable computer readable storage medium. Furthermore,the series of instructions need not be stored locally, and could bereceived from a remote storage device, such as a server on a network,via the network interface 716. The instructions are copied from thestorage device, such as the mass storage 718, into the system memory 714and then accessed and executed by the processor 702. In variousimplementations, a module or modules can be executed by a processor ormultiple processors in one or multiple locations, such as multipleservers in a parallel processing environment.

Examples of computer-readable media include, but are not limited to,recordable type media such as volatile and non-volatile memory devices;solid state memories; floppy and other removable disks; hard diskdrives; magnetic media; optical disks (e.g., Compact Disk Read-OnlyMemory (CD ROMS), Digital Versatile Disks (DVDs)); other similarnon-transitory (or transitory), tangible (or non-tangible) storagemedium; or any type of medium suitable for storing, encoding, orcarrying a series of instructions for execution by the computer system700 to perform any one or more of the processes and features describedherein.

For purposes of explanation, numerous specific details are set forth inorder to provide a thorough understanding of the description. It will beapparent, however, to one skilled in the art that embodiments of thedisclosure can be practiced without these specific details. In someinstances, modules, structures, processes, features, and devices areshown in block diagram form in order to avoid obscuring the description.In other instances, functional block diagrams and flow diagrams areshown to represent data and logic flows. The components of blockdiagrams and flow diagrams (e.g., modules, blocks, structures, devices,features, etc.) may be variously combined, separated, removed,reordered, and replaced in a manner other than as expressly describedand depicted herein.

Reference in this specification to “one embodiment”, “an embodiment”,“other embodiments”, “one series of embodiments”, “some embodiments”,“various embodiments”, or the like means that a particular feature,design, structure, or characteristic described in connection with theembodiment is included in at least one embodiment of the disclosure. Theappearances of, for example, the phrase “in one embodiment” or “in anembodiment” in various places in the specification are not necessarilyall referring to the same embodiment, nor are separate or alternativeembodiments mutually exclusive of other embodiments. Moreover, whetheror not there is express reference to an “embodiment” or the like,various features are described, which may be variously combined andincluded in some embodiments, but also variously omitted in otherembodiments. Similarly, various features are described that may bepreferences or requirements for some embodiments, but not otherembodiments.

The language used herein has been principally selected for readabilityand instructional purposes, and it may not have been selected todelineate or circumscribe the inventive subject matter. It is thereforeintended that the scope of the invention be limited not by this detaileddescription, but rather by any claims that issue on an application basedhereon. Accordingly, the disclosure of the embodiments of the inventionis intended to be illustrative, but not limiting, of the scope of theinvention, which is set forth in the following claims.

What is claimed is:
 1. A computer-implemented method comprising: obtaining, by a computing system, a first video frame and a second video frame; processing, by the computing system, the first video frame using a convolutional neural network to output a first set of feature maps; processing, by the computing system, the second video frame using the convolutional neural network to output a second set of feature maps; and processing, by the computing system, the first set of feature maps and the second set of feature maps using a spatial matching layer of the convolutional neural network to determine an optical flow for at least one pixel.
 2. The computer-implemented method of claim 1, wherein processing the first set of feature maps and the second set of feature maps using the spatial matching layer of the convolutional neural network further comprises: determining, by the computing system, an optical flow for the pixel along an axis by averaging i) a first displacement measurement of the pixel across a first feature map in the first set of feature maps and a first feature map in the second set of feature maps and ii) a second displacement measurement of the pixel across a second feature map in the first set of feature maps and a second feature map in the second set of feature maps.
 3. The computer-implemented method of claim 2, wherein determining the optical flow for the pixel along the axis further comprises: determining, by the computing system, a correspondence between at least one pixel in the first feature map in the first set and at least one pixel the first feature map in the second set; determining, by the computing system, the first displacement measurement of the corresponding pixel between the first feature map in the first set and the first feature map in the second set along the axis; determining, by the computing system, a correspondence between at least one pixel in the second feature map in the first set and at least one pixel the second feature map in the second set; and determining, by the computing system, the second displacement measurement of the pixel between the second feature map in the first set and the second feature map in the second set along the axis.
 4. The computer-implemented method of claim 1, wherein processing the first set of feature maps and the second set of feature maps using the spatial matching layer of the convolutional neural network further comprises: determining, by the computing system, an optical flow for the pixel along an axis based at least in part on a histogram that includes i) a first displacement measurement of the pixel across a first feature map in the first set of feature maps and a first feature map in the second set of feature maps and ii) a second displacement measurement of the pixel across a second feature map in the first set of feature maps and a second feature map in the second set of feature maps.
 5. The computer-implemented method of claim 4, wherein determining the optical flow for the pixel along the axis further comprises: generating, by the computing system, the histogram using the first displacement measurement and the second displacement measurement, wherein the optical flow for the pixel along the axis based at least in part on a maximum peak value in the histogram.
 6. The computer-implemented method of claim 1, wherein the optical flow for the pixel provides at least a predicted direction of the pixel along an x-axis and a predicted direction of the pixel along a y-axis.
 7. The computer-implemented method of claim 1, wherein the optical flow for the pixel provides at least a predicted magnitude of the pixel along an x-axis and a predicted magnitude of the pixel along a y-axis.
 8. The computer-implemented method of claim 1, the method further comprising: training, by the computing system, the convolutional neural network using one or more optical flow training data sets.
 9. The computer-implemented method of claim 8, the method further comprising: processing, by the computing system, a first video frame in at least one training data set using the convolutional neural network to output a first set of test feature maps; processing, by the computing system, a second video frame in the at least one training data set using the convolutional neural network to output a second set of test feature maps; processing, by the computing system, the first set of test feature maps and the second set of test feature maps using the spatial matching layer of the convolutional neural network to determine an optical flow for at least one pixel; determining, by the computing system, at least one inaccuracy in the optical flow for the pixel based on a ground truth optical flow for the pixel; and adjusting, by the computing system, one or more weight values of one or more filters associated with the convolutional neural network to minimize the inaccuracy.
 10. The computer-implemented method of claim 1, wherein processing, by the computing system, the first video frame using the convolutional neural network to output the first set of feature maps further comprises: inputting, by the computing system, a representation of the first video frame to at least one convolutional layer to output a set of signals, the convolutional layer being trained to apply at least one convolutional operation to the representation of the first video frame, wherein the at least one convolutional operation is based on one or more filters to convolve the representation of the first video frame, the one or more filters being weighted to predict an optical flow for one or more pixels.
 11. A system comprising: at least one processor; and a memory storing instructions that, when executed by the at least one processor, cause the system to perform: obtaining a first video frame and a second video frame; processing the first video frame using a convolutional neural network to output a first set of feature maps; processing the second video frame using the convolutional neural network to output a second set of feature maps; and processing the first set of feature maps and the second set of feature maps using a spatial matching layer of the convolutional neural network to determine an optical flow for at least one pixel.
 12. The system of claim 11, wherein processing the first set of feature maps and the second set of feature maps using the spatial matching layer of the convolutional neural network further causes the system to perform: determining an optical flow for the pixel along an axis by averaging i) a first displacement measurement of the pixel across a first feature map in the first set of feature maps and a first feature map in the second set of feature maps and ii) a second displacement measurement of the pixel across a second feature map in the first set of feature maps and a second feature map in the second set of feature maps.
 13. The system of claim 12, wherein determining the optical flow for the pixel along the axis further causes the system to perform: determining a correspondence between at least one pixel in the first feature map in the first set and at least one pixel the first feature map in the second set; determining, by the computing system, the first displacement measurement of the corresponding pixel between the first feature map in the first set and the first feature map in the second set along the axis; determining, by the computing system, a correspondence between at least one pixel in the second feature map in the first set and at least one pixel the second feature map in the second set; and determining, by the computing system, the second displacement measurement of the pixel between the second feature map in the first set and the second feature map in the second set along the axis.
 14. The system of claim 11, wherein processing the first set of feature maps and the second set of feature maps using the spatial matching layer of the convolutional neural network further causes the system to perform: determining an optical flow for the pixel along an axis based at least in part on a histogram that includes i) a first displacement measurement of the pixel across a first feature map in the first set of feature maps and a first feature map in the second set of feature maps and ii) a second displacement measurement of the pixel across a second feature map in the first set of feature maps and a second feature map in the second set of feature maps.
 15. The system of claim 14, wherein determining the optical flow for the pixel along the axis further causes the system to perform: generating the histogram using the first displacement measurement and the second displacement measurement, wherein the optical flow for the pixel along the axis based at least in part on a maximum peak value in the histogram.
 16. A non-transitory computer-readable storage medium including instructions that, when executed by at least one processor of a computing system, cause the computing system to perform a method comprising: obtaining a first video frame and a second video frame; processing the first video frame using a convolutional neural network to output a first set of feature maps; processing the second video frame using the convolutional neural network to output a second set of feature maps; and processing the first set of feature maps and the second set of feature maps using a spatial matching layer of the convolutional neural network to determine an optical flow for at least one pixel.
 17. The non-transitory computer-readable storage medium of claim 16, wherein processing the first set of feature maps and the second set of feature maps using the spatial matching layer of the convolutional neural network further causes the computing system to perform: determining an optical flow for the pixel along an axis by averaging i) a first displacement measurement of the pixel across a first feature map in the first set of feature maps and a first feature map in the second set of feature maps and ii) a second displacement measurement of the pixel across a second feature map in the first set of feature maps and a second feature map in the second set of feature maps.
 18. The non-transitory computer-readable storage medium of claim 17, wherein determining the optical flow for the pixel along the axis further causes the computing system to perform: determining a correspondence between at least one pixel in the first feature map in the first set and at least one pixel the first feature map in the second set; determining, by the computing system, the first displacement measurement of the corresponding pixel between the first feature map in the first set and the first feature map in the second set along the axis; determining, by the computing system, a correspondence between at least one pixel in the second feature map in the first set and at least one pixel the second feature map in the second set; and determining, by the computing system, the second displacement measurement of the pixel between the second feature map in the first set and the second feature map in the second set along the axis.
 19. The non-transitory computer-readable storage medium of claim 16, wherein processing the first set of feature maps and the second set of feature maps using the spatial matching layer of the convolutional neural network further causes the system to perform: determining an optical flow for the pixel along an axis based at least in part on a histogram that includes i) a first displacement measurement of the pixel across a first feature map in the first set of feature maps and a first feature map in the second set of feature maps and ii) a second displacement measurement of the pixel across a second feature map in the first set of feature maps and a second feature map in the second set of feature maps.
 20. The non-transitory computer-readable storage medium of claim 19, wherein determining the optical flow for the pixel along the axis further causes the system to perform: generating the histogram using the first displacement measurement and the second displacement measurement, wherein the optical flow for the pixel along the axis based at least in part on a maximum peak value in the histogram. 